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A blend of methods of recursion theory and topology

Iraj Kalantari, Larry Welch
2003 Annals of Pure and Applied Logic  
While in those papers we developed groundwork for an approach to point free analysis and applied recursion theory, in this paper we blend techniques of recursion theory with those of topology to establish  ...  This paper is a culmination of our new foundations for recursive analysis through recursive topology as reported in Kalantari and Welch (Ann Pure Appl. Logic 93 (1998) 125; 98 (1999) 87).  ...  Klaus Weihrauch for proÿtable conversations and encouragement since the distribution of the ÿrst manuscript.  ... 
doi:10.1016/s0168-0072(03)00054-x fatcat:5gdbu6f2dvhg7obv2nrzk5jhau

Artificial Cognitively-inspired Generation of the Notion of Topological Group in the Context of Artificial Mathematical Intelligence [article]

Danny A. J. Gomez-Ramirez, Yoe A. Herrera-Jaramillo, Florian Geismann
2021 arXiv   pre-print
Specifically, we start with two basic notions belonging to topology and abstract algebra, and we describe recursively formal specifications in the Common Algebraic Specification Language (CASL).  ...  The fundamental notion of topological groups is explicitly generated through three different artificial specifications based on conceptual blending and conceptual identification, starting with the concepts  ...  Acknowledgements The second author thank the Universidad Autonoma de Bucaramanga for all the support (Grant I56073) and the Institución Universitaria Tecnológico de Antioquia. Danny A. J.  ... 
arXiv:2112.02457v1 fatcat:cd7v4fthtngjpmi4noacdvyjku

Evidence and Limits of Universal Topological Surface Segregation of Cyclic Polymers

Qiming He, Shih-Fan Wang, Renfeng Hu, Bulent Akgun, Caleb Tormey, Somesh Peri, David T. Wu, Mark D. Foster
2017 Physical Review Letters  
Twenty years ago it was proposed that a universal topological driving force would drive cyclic chains to enrich the surface of blends of linear and cyclic chains.  ...  Both blends containing branched chains [14] [15] [16] [17] and blends containing cyclic polymers [18] are of practical interest and the behaviors of these two sorts of topological blends are expected  ... 
doi:10.1103/physrevlett.118.167801 pmid:28474912 fatcat:4lui6lfvnvdl5n4hhzbbz6fa5e

Page 5967 of Mathematical Reviews Vol. , Issue 2004h [page]

2004 Mathematical Reviews  
of sets below 0’.” 2004h:03127 03F60 03C57 03D45 03D80 54A20 Kalantari, Iraj (1-WIL; Macomb, IL); Welch, Larry (1-WIL; Macomb, IL) A blend of methods of recursion theory and topology.  ...  The paper is the third in a series of papers by the authors on a foundation for recursive analysis which is motivated by point- free topology, the others being [Ann. Pure Appl.  ... 

A Framework of Stability Analysis for Multi-agent Systems on Arbitrary Topology Graph: Linear Systems [article]

Wang Yong, Li Guiming
2015 arXiv   pre-print
Through transforming the construction of a graph into a standard procedure only including three basic structures, the stability analysis is recursive and independent of the specific topology.  ...  Different from the general tools: the Laplacian matrix based method and the Lyapunov's method, this approach treats the multi-agent system as the composition of many isolated agents, and focuses on their  ...  Adding one agent to the consensus MAS G k−1 in one of 3 basic topologies yields a consensus MAS G k In this section, we will introduce three basic topologies and prove the above recursive process.  ... 
arXiv:1504.04240v1 fatcat:wkq6bdkc2vfatmhjhto62fi24u

Algorithmic Aspects of Theory Blending [chapter]

Maricarmen Martinez, Ulf Krumnack, Alan Smaill, Tarek Richard Besold, Ahmed M. H. Abdel-Fattah, Martin Schmidt, Helmar Gust, Kai-Uwe Kühnberger, Markus Guhe, Alison Pease
2014 Lecture Notes in Computer Science  
This paper describes a logic-based framework which allows a formal treatment of theory blending, discusses algorithmic aspects of blending within the framework, and provides an illustrating worked out  ...  It thereby provides a possible theoretical foundation for modeling high-level cognitive faculties such as the ability to understand, learn, and create new concepts and theories.  ...  We will propose two alternative competing criteria for structural blend optimality that also work in the spirit of the Web, Unpacking, and Topology principles, and an algorithmic method for performing  ... 
doi:10.1007/978-3-319-13770-4_16 fatcat:tkkfz3guxbeaplzmpj62i2sfie

Page 77 of University Computing : The Bulletin of the IUCC Vol. 12, Issue 2 [page]

1990 University Computing : The Bulletin of the IUCC  
Vickers has collected in one volume a large number of theoretical results and blended them together to generate a coherent exposition of the application of topology to the mathematics of computation.  ...  Treatments of topological system construction, point logic, compactness and. domain theory follow and Vickers ends with an examination of the spectra of rings for those readers with a particular interest  ... 

Page 140 of Mathematical Reviews Vol. , Issue 90A [page]

1990 Mathematical Reviews  
In the early 1970s Macintyre introduced a cocktail of methods from group theory, recursion theory and model theory for studying the possible sets Sk(G).  ...  Study of these semigroups pro- 20 GROUP THEORY AND GENERALIZATIONS 140 vides a beautiful blend of abstract semigroup theory and algebraic geometry.  ... 

Computable algebra, general theory and theory of computable fields

Michael O. Rabin
1960 Transactions of the American Mathematical Society  
In this paper we follow a similar program and study a blend of algebra and theory of recursive functions.  ...  The basic definitions and the concepts studied are a blend of algebra and topology. Thus we are most interested in those homorphisms which are also continuous mappings.  ...  In this paper we follow a similar program and study a blend of algebra and theory of recursive functions.  ... 
doi:10.1090/s0002-9947-1960-0113807-4 fatcat:drbyhc6ma5deveuadanxiylj7q

A Celtic Framework for Knots and Links

Jonathan L. Gross, Thomas W. Tucker
2010 Discrete & Computational Geometry  
This involves a confluence of ideas from knot theory, topological graph theory, and the theory of orthogonal graph drawings.  ...  We use medial graphs and graph minors to prove, conversely, that every alternating projection of a link is topologically equivalent to some Celtic link, specifiable by this method.  ...  Our exploration herein of Celtic knots blends knot theory, topological graph theory, and discrete geometry, with applications to computer graphics.  ... 
doi:10.1007/s00454-010-9257-0 fatcat:msvybstqxbfktbit3pombl4hiu

Book Review: Recursion-theoretic hierarchies

Keith J. Devlin
1980 Bulletin of the American Mathematical Society  
After some preliminaries concerning basic logic and set theory, topology and measure, and inductive definitions, the notions of primitive recursion, recursive functional, and recursive relation are defined  ...  The author is clearly addressing himself to more advanced students, a reasonable knowledge of analysis, topology, measure theory, set theory and logic being a prerequisite for the book.  ... 
doi:10.1090/s0273-0979-1980-14714-x fatcat:7sac7p3gd5e53nv4ygaqr7n7wy

Page 3728 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
Verlan, An explicit method of bidimensional C?? interpolation using splines (545-556); Marius Zimand, On the topological size of p-m-complete degrees (557-565).  ...  Slabu, A recursive approach of the algorithms complexity (1-11); Jiirgen Dassow and Gheorghe Paun, On the power of cooperation in dis- tributed grammar systems (12-23); Adrian Atanasiu and Victor Mitrana  ... 

Helical edge and surface states in HgTe quantum wells and bulk insulators

Xi Dai, Taylor L. Hughes, Xiao-Liang Qi, Zhong Fang, Shou-Cheng Zhang
2008 Physical Review B  
The quantum spin Hall (QSH) effect is the property of a new state of matter which preserves time-reversal, has an energy gap in the bulk, but has topologically robust gapless states at the edge.  ...  We also show that 3d HgTe is a topological insulator under uniaxial strain, and show that the surface states are described by single-component massless relativistic Dirac fermions in 2+1 dimensions.  ...  By the recursion method we obtain the charge and spin density of states defined above.  ... 
doi:10.1103/physrevb.77.125319 fatcat:qoxsjdcrejf7lmez7pgsorr3ou

Geodesic Mapping for Dynamic Surface Alignment

Tony Tung, Takashi Matsuyama
2014 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The coordinates are used to recursively choose correspondence points in non-ambiguous regions using a coarse-to-fine strategy to reliably locate all surface points and define a discrete mapping.  ...  The proposed framework consists of a geodesic mapping (i.e., geodesic diffeomorphism) between surfaces which carry a distance function (namely the global geodesic distance), and a geodesic-based coordinate  ...  ACKNOWLEDGMENTS This work was supported in part by the JST-CREST project "Creation of Human-Harmonized Information Technology for Convivial Society".  ... 
doi:10.1109/tpami.2013.179 pmid:26353225 fatcat:zlu5gsehevednnzxdpvxgriivy

Geometrically accurate, efficient, and flexible quadrature techniques for the tetrahedral finite cell method

Atanas Stavrev, Lam H. Nguyen, Ruyi Shen, Vasco Varduhn, Marek Behr, Stefanie Elgeti, Dominik Schillinger
2016 Computer Methods in Applied Mechanics and Engineering  
The elementwise parametrization procedure relies on the identification of the intersection topology and a series of higher-order mappings based on Lagrange polynomials.  ...  We consider the tetrahedral finite cell method (TetFCM) and replace its recursive subdivision based integration approach with geometrically accurate quadrature rules that emanate from higher-order geometric  ...  The Minnesota group gratefully acknowledges support from the National Science Foundation (CISE-1565997) and the In-  ... 
doi:10.1016/j.cma.2016.07.041 fatcat:pcmhdsxn2rehjhozzbjzrstfha
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